Solve the Inequality for x 5^(2x+1)<=125

$5^{2 x + 1} \leq 125$

Create equivalent expressions in the equation that all have equal bases.

$5^{2 x + 1} \leq 5^{3}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 x + 1 \leq 3$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the inequality.

Subtract $1$ from both sides of the inequality.

$2 x \leq 3 - 1$

Subtract $1$ from $3$ .

$2 x \leq 2$

Divide each term in $2 x \leq 2$ by $2$ and simplify.

Divide each term in $2 x \leq 2$ by $2$ .

$\frac{2 x}{2} \leq \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{2}{2}$

Divide $x$ by $1$ .

$x \leq \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

$x \leq 1$

The result can be shown in multiple forms.

Inequality Form:

$x \leq 1$

Interval Notation:

$(- \infty, 1]$